The pressure acting on 500 cubic meters of gas is reduced from 4 atm to 2 atm. If the temperature remains constant, what is the new volume?

1 Answer
Mar 2, 2016

Answer:

#"V"_"new"="1000 m"^3#

Explanation:

We will use Boyle's law, which states that pressure and volume are inversely proportional at constant temperature. We can express this mathematically as:

#"P"_1"V"_1="P"_2"V"_2#

Here, we see that

#"P"_1="4 atm"#
#"P"_2="2 atm"#

#"V"_1="500 m"^3#
#"V"_2="unknown"#

We want to manipulate Boyle's law to solve for #"V"_2#:

#"V"_2=("P"_1"V"_1)/("P"_2)#

Plugging in what we know:

#"V"_2=("4 atm" * "500 m"^3)/("2 atm")#

#"V"_2=2 * "500 m"^3#

#"V"_2="1000 m"^3#

We can see that the volume increased from #"500 m"^3# to #"1000 m"^3#, so it doubled. This is paired with the pressure being halved, as should be the case in an inversely proportional relationship.